Subgroups — C₁₉×#23556 #18029515

Order 4864.

1110 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2059	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2058	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#544	—	2	4	no	—
13	C₁₉×#544	—	2	4	no	—
14	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×#125	—	2	1	no	—
17	C₂×C₁₉×#125	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#428	—	2	4	no	—
25	C₂×C₁₉×#107	C₂²	1	2	yes	—
26	C₂×C₁₉×#106	—	2	4	no	—
27	C₂×C₁₉×#106	C₂²	1	2	yes	—
28	C₂×C₁₉×#106	C₂²	1	4	yes	—
29	C₁₉×#389	C₂²	1	4	yes	—
30	C₁₉×#385	—	2	2	no	—
31	C₁₉×#384	—	2	1	no	—
32	C₁₉×#382	—	2	1	no	—
33	C₁₉×#340	C₂²	1	2	yes	—
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	4	yes	—
36	C₁₉×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₉	—	2	2	no	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	—	2	1	no	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₁₉	—	2	2	no	—
42	C₂×M₁₆×C₁₉	—	2	2	no	—
43	C₂×M₁₆×C₁₉	Q₈	1	4	yes	complemented
44	C₂²×C₈×C₁₉	—	2	2	no	—
45	C₂²×C₈×C₁₉	—	2	2	no	—
46	C₂²×C₈×C₁₉	Q₈	1	4	yes	complemented
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
49	C₁₉×C₄⋊Q₈	—	2	8	no	—
50	C₁₉×C₄⋊Q₈	—	2	4	no	—
51	C₁₉×C₄⋊Q₈	—	2	4	no	—
52	C₁₉×#125	—	2	8	no	—
53	C₁₉×#125	—	2	4	no	—
54	C₁₉×#125	—	2	4	no	—
55	C₁₉×C₂²⋊Q₈	—	2	16	no	—
56	C₁₉×#117	—	2	2	no	—
57	C₁₉×#117	—	2	2	no	—
58	C₁₉×#117	—	2	2	no	—
59	C₁₉×#117	—	2	2	no	—
60	C₁₉×#117	D₄	1	4	yes	—
61	C₁₉×#117	Q₈	1	4	yes	complemented
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
85	C₁₉×#107	—	2	4	no	—
86	C₁₉×#106	—	2	8	no	—
87	C₁₉×#106	—	2	4	no	—
88	C₁₉×#95	—	2	4	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₁₉	—	2	8	no	—
91	C₂×Q₈×C₁₉	—	8	4	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	8	2	no	—
100	C₂²×C₄×C₁₉	—	8	2	no	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₉	#41	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₉	—	2	8	no	—
112	C₂×C₈×C₁₉	—	2	8	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	2	2	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
118	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
119	C₄⋊C₄×C₁₉	—	2	8	no	—
120	C₄⋊C₄×C₁₉	—	2	8	no	—
121	C₄⋊C₄×C₁₉	—	2	8	no	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	—	2	1	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	4	2	no	—
132	C₄⋊C₄×C₁₉	—	8	4	no	—
133	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
134	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
137	C₂²⋊C₄×C₁₉	—	2	4	no	—
138	C₂²⋊C₄×C₁₉	—	2	4	no	—
139	C₂²⋊C₄×C₁₉	—	2	4	no	—
140	C₄²×C₁₉	—	2	4	no	—
141	C₄²×C₁₉	—	2	4	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	#23556	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	#120	1	2	yes	—
148	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
149	C₂³×C₁₉	C₄⋊Q₈	1	2	yes	—
150	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₉	—	8	8	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	8	4	no	—
168	C₂×C₄×C₁₉	—	8	4	no	—
169	C₂×C₄×C₁₉	#120	1	2	yes	—
170	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
171	C₂×C₄×C₁₉	C₂²⋊Q₈	1	4	yes	—
172	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
174	C₂×C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
175	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
176	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
182	C₈×C₁₉	—	2	4	no	—
183	C₈×C₁₉	—	2	4	no	—
184	C₂×#544	C₂×C₁₉	1	1	yes	characteristic
185	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
186	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic
187	#2317	C₂×C₁₉	1	1	yes	characteristic
188	#2059	C₂×C₁₉	1	4	yes	complemented
189	#2058	C₂×C₁₉	1	4	yes	complemented
190	#1736	C₂×C₁₉	1	1	yes	characteristic
191	#1735	C₂×C₁₉	1	1	yes	characteristic
192	#1729	C₂×C₁₉	1	1	yes	characteristic
193	C₂²×C₁₉	—	2	4	no	—
194	C₂²×C₁₉	—	2	4	no	—
195	C₂²×C₁₉	—	2	2	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	#395	1	4	yes	—
198	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
199	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
200	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
201	C₂²×C₁₉	#577	1	2	yes	—
202	C₂²×C₁₉	#577	1	2	yes	—
203	C₄×C₁₉	—	4	4	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	4	2	no	—
208	C₄×C₁₉	—	4	2	no	—
209	C₄×C₁₉	—	8	2	no	—
210	C₄×C₁₉	#395	1	4	yes	—
211	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
212	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
214	C₄×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
216	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
217	#544	—	2	4	no	—
218	#544	—	2	4	no	—
219	C₂×C₄⋊Q₈	—	2	1	no	—
220	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
221	C₂×#125	—	2	1	no	—
222	C₂×#125	C₂²×C₁₉	1	2	yes	—
223	C₂×C₂²⋊Q₈	—	2	2	no	—
224	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
229	#428	—	2	4	no	—
230	C₂×#107	C₂²×C₁₉	1	2	yes	—
231	C₂×#106	—	2	4	no	—
232	C₂×#106	C₂²×C₁₉	1	2	yes	—
233	C₂×#106	C₂²×C₁₉	1	4	yes	—
234	#389	C₂²×C₁₉	1	4	yes	—
235	#385	—	2	2	no	—
236	#384	—	2	1	no	—
237	#382	—	2	1	no	—
238	#340	C₂²×C₁₉	1	2	yes	—
239	#340	C₂²×C₁₉	1	4	yes	—
240	#340	C₂²×C₁₉	1	2	yes	—
241	#336	C₂²×C₁₉	1	4	yes	—
242	C₂×C₁₉	—	2	4	no	—
243	C₂×C₁₉	C₂×#395	1	1	yes	characteristic
244	C₂×C₁₉	#3009	1	1	yes	characteristic
245	C₂×C₁₉	#3010	1	1	yes	characteristic
246	C₂×C₁₉	#3084	1	2	yes	—
247	C₂×C₁₉	#3163	1	2	yes	—
248	C₂²×Q₈	—	2	2	no	—
249	C₂³×C₄	—	2	1	no	—
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	Q₈×C₁₉	1	4	yes	complemented
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	Q₈×C₁₉	1	4	yes	complemented
258	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
259	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
260	C₄⋊Q₈	—	2	8	no	—
261	C₄⋊Q₈	—	2	4	no	—
262	C₄⋊Q₈	—	2	4	no	—
263	#125	—	2	8	no	—
264	#125	—	2	4	no	—
265	#125	—	2	4	no	—
266	C₂²⋊Q₈	—	2	16	no	—
267	#117	—	2	2	no	—
268	#117	—	2	2	no	—
269	#117	—	2	2	no	—
270	#117	—	2	2	no	—
271	#117	D₄×C₁₉	1	4	yes	—
272	#117	Q₈×C₁₉	1	4	yes	complemented
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
283	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
296	#107	—	2	4	no	—
297	#106	—	2	8	no	—
298	#106	—	2	4	no	—
299	#95	—	2	4	no	—
300	C₁₉	#23556	1	1	yes	characteristic, direct product factor, Sylow
301	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	8	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	8	2	no	—
312	C₂²×C₄	—	8	2	no	—
313	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
318	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
319	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
321	C₂²×C₄	#41×C₁₉	1	2	yes	—
322	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
323	M₁₆	—	2	8	no	—
324	C₂×C₈	—	2	8	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
330	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	8	4	no	—
345	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
346	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
347	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₄²	—	2	4	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	C₁₉×#120	1	2	yes	—
359	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
360	C₂³	C₁₉×C₄⋊Q₈	1	2	yes	—
361	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
362	Q₈	—	8	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	8	4	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	C₁₉×#120	1	2	yes	—
381	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
382	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
383	C₂×C₄	C₁₉×C₂²⋊Q₈	1	4	yes	—
384	C₂×C₄	C₁₉×C₄⋊Q₈	1	2	yes	—
385	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
386	C₂×C₄	C₁₉×C₄⋊Q₈	1	4	yes	—
387	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
391	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
393	C₈	—	2	4	no	—
394	C₈	—	2	4	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	C₁₉×#395	1	4	yes	—
400	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
401	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
402	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
403	C₂²	C₁₉×#577	1	2	yes	—
404	C₂²	C₁₉×#577	1	2	yes	—
405	C₄	—	4	2	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	4	no	—
411	C₄	—	8	2	no	—
412	C₄	C₁₉×#395	1	4	yes	—
413	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
414	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
415	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
416	C₄	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
417	C₂	—	2	4	no	—
418	C₂	C₂×C₁₉×#395	1	1	yes	characteristic
419	C₂	C₁₉×#3009	1	1	yes	characteristic
420	C₂	C₁₉×#3010	1	1	yes	characteristic
421	C₂	C₁₉×#3084	1	2	yes	—
422	C₂	C₁₉×#3163	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₁₉×#2059	C₂	semidirect
6. C₁₉×#2058	C₂	semidirect
43. C₂×M₁₆×C₁₉	Q₈	semidirect
46. C₂²×C₈×C₁₉	Q₈	semidirect
61. C₁₉×#117	Q₈	semidirect
144. #23556	C₁₉	direct (N × H)
188. #2059	C₂×C₁₉	semidirect
189. #2058	C₂×C₁₉	semidirect
254. C₂×M₁₆	Q₈×C₁₉	semidirect
257. C₂²×C₈	Q₈×C₁₉	semidirect
272. #117	Q₈×C₁₉	semidirect
300. C₁₉	#23556	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#544	2
C₂×C₁₉×#428	2
C₂²×C₁₉×#106	2
C₁₉×#2317	2
C₁₉×#2059	2
C₁₉×#2058	2
C₁₉×#1736	2
C₁₉×#1735	2
C₁₉×#1729	2
#23556	19

Subgroups — C19×#23556 #18029515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23556 #18029515